Experimental Protocol for Comparative Testing of Consistency Constraints in Post-Selected Quantum Circuits: A Comparative NISQ Study

Complete experimental protocol (Project Rhea) for comparative testing of post-selected "consistency-constrained" circuits on NISQ hardware using matched A/B/C/D controls. This document provides a rigorously designed blueprint for testing whether enforcing causal-consistency constraints via post-selection introduces distinctive instability or resource costs beyond standard device noise. The protocol features: • Strict A/B/C/D comparative design (Constrained / Unconstrained / Baseline / Rare-event control)• Pre-registered statistical thresholds and decision criteria• Conservative interpretation framework ("ordinary explanations first" escalation ladder)• Resource estimates for IBM Quantum and IonQ cloud platforms• Order-of-magnitude shot budgets and sample size calculations• Reproducibility checklist and data release plan The author lacks direct hardware access and releases this under CC BY 4.0 to invite experimental collaborators for implementation. Target: quantum benchmarking, post-selection studies, quantum foundations, and NISQ experimental methodology. Keywords: NISQ, post-selection, quantum benchmarking, A/B testing, consistency constraints, P-CTC